This was further corroborated by the good match between the predicted and observed population stage-structure.
Therefore, it is more practical to consider the population model with stage structure when establishing the mathematical model.
This paper gives an analytical proof of the existence of chaotic dynamics for a single-species discrete population model with stage structure and birth pulses.
Population models with stage structure have been investigated by many researchers, and various methods and techniques have been used to study the existence and qualitative properties of solutions [1 9].
According to model (1), they proposed the discrete single-species population model with stage structure textstylebegin{cases} x_{n+1}=x_{n}+bmathrm{e}^{- x_{n}+y_{n})}y_{n}-d_{1}x_{n}-delta x_{n}, y_{n+1}=y_{n}+delta x_{n}-d_{2}y_{n}, end{cases}displaystyle nin N_{0}, (2) where (N_{0}) denotes the set of non-negative integers.
In 2005, Gao and Chen [10] proposed a single-species discrete population model with stage structure and birth pulses: { u n + 1 = r u n + b e − ( r + p ) u n − q v n ( p u n + q v n ), v n + 1 = p u n + q v n, (1.1).
Straightforward computations show that conditions (3.1), (3.2) in Theorem 3.2 hold for r = 0.003, p = 0.597, q = 1.5 × 10 − 7, b = exp ( 3.2 ) / p. This paper rigorously proves the existence of chaotic dynamics for a single-species discrete population model with stage structure and birth pulses.
Eight species were parameterised to broadly represent different stage structure, population densities and modes of dispersal.
In this paper, we study a stage structure population model with fixed-time birth pulse and state feedback control strategy.
Outputs of the model include the asymptotic population growth rate, stable stage structure and asymptotic spatial distribution that allow comparison of the influence of different spatial scenarios of wood fragmentation on population dynamics.
The exceptions are age and stage; the age or stage structure of populations (the fraction of individuals in each age or developmental stage class) is sometimes incorporated in the traditional models of population ecology.
